A281358 Number of scenarios in the Gift Exchange Game when a gift can be stolen at most 6 times.

1, 7, 6427, 216864652, 60790021361170, 79397199549271412737, 350521520018942991464535019, 4247805448772073978048752721163278, 122022975450467092259059357046375920848764, 7449370563518425038119522091529589590475534631830

Offset: 0

Author

N. J. A. Sloane, Jan 25 2017

Keywords

• nonn

Comments

The result from the recurrence has been confirmed up to a(63) by using an optimized version of equation (23) in the Applegate-Sloane paper. - Lars Blomberg, Feb 01 2017

Links

• Lars Blomberg, Table of n, a(n) for n = 0..88
• Moa Apagodu, David Applegate, N. J. A. Sloane, and Doron Zeilberger, Analysis of the Gift Exchange Problem, arXiv:1701.08394 [math.CO], 2017.
• Moa Apagodu, David Applegate, N. J. A. Sloane, and Doron Zeilberger, On-Line Appendix I to "Analysis of the gift exchange problem", giving Type D recurrences for G_1(n) through G_15(n) (see A001515, A144416, A144508, A144509, A149187, A281358-A281361)
• Moa Apagodu, David Applegate, N. J. A. Sloane, and Doron Zeilberger, On-Line Appendix II to "Analysis of the gift exchange problem", giving Type C recurrences for G_1(n) through G_15(n) (see A001515, A144416, A144508, A144509, A149187, A281358-A281361)
• David Applegate and N. J. A. Sloane, The Gift Exchange Problem, arXiv:0907.0513 [math.CO], 2009.

Crossrefs

The gift scenarios sequences when a gift can be stolen at most s times, for s = 1..9, are A001515, A144416, A144508, A144509, A149187, A281358, A281359, A281360, A281361.

Programs

Maple

with(combinat):
b:= proc(n, i, t) option remember; `if`(t*i add(b(k, 7, n), k=0..7*n):
seq(a(n), n=0..12);  # Alois P. Heinz, Feb 01 2017

Mathematica

t[n_, n_] = 1; t[n_ /; n >= 0, k_] /; 0 <= k <= 7*n := t[n, k] = Sum[(1/j!)*Product[k - m, {m, 1, j}]*t[n - 1, k - j - 1], {j, 0, 6}]; t[, ] = 0; a[n_] := Sum[t[n, k], {k, 0, 7*n}]; Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Feb 18 2017 *)

PARI

{a(n) = sum(i=n, 7*n, i!*polcoef(sum(j=1, 7, x^j/j!)^n, i))/n!} \\ Seiichi Manyama, May 22 2019

Extensions

More terms from Lars Blomberg, Feb 01 2017